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NaN-safe mode is not NaN-safe enough #774
Description
NaN-safe mode is actually not NaN-safe enough.
With NaN-safe mode enabled:
julia> using ForwardDiff
julia> log(ForwardDiff.Dual{:tag}(0.0, 0.0))
Dual{:tag}(-Inf,0.0)
julia> log(ForwardDiff.Dual{:tag}(0.0, 0.0, 1.0))
Dual{:tag}(-Inf,NaN,Inf)This can be triggered also using the ForwardDiff API:
julia> ForwardDiff.derivative(log ∘ zero, 1.0)
0.0
julia> f(x) = log(zero(x[1]) + x[2])
f (generic function with 1 method)
julia> ForwardDiff.gradient(f, [1.0, 0.0])
2-element Vector{Float64}:
NaN
InfThe problem is that NaN-safe mode checks whether ALL partials are zero whereas actually it should be applied for each zero partial. Thus one can work around the issue by enforcing that there's only one partial:
julia> ForwardDiff.gradient(f, [1.0, 0.0], ForwardDiff.GradientConfig(f, [1.0, 0.0], ForwardDiff.Chunk{1}()))
2-element Vector{Float64}:
0.0
InfEdit: Another instance of this issue is #745
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